Unit Circle
In what quadrant is the angle (5pi)/4
Quadrant III
What is tanpi/2?
Undefined
y=-sin((2pix)/3) What is the amplitude, period, horizontal and vertical shift
Amplitude is 1, period is 3, horizontal and vertical shifts are 0
Find the exact value of the expression
cos(pi/4+pi/3)
1/4(sqrt(2)-sqrt(6))
tanx sec^2x = tanx tan^2x + 1
Is this a legal move? Explain.
No.
tanx sec^2x = tanx (tan^2x + 1)
What is the positive and negative coterminal angle of (4pi)/3
(10pi)/3 and -(2pi)/3
What is tan^-1(-1)
-pi/4
Where is the domain and range of the graph
y=2+5cos(6pix)
domain is all real numbers
range is -3 <= y <= 7
Find the exact AND simplest value of the expression
sin 100° cos 40° − cos 100° sin 40°
sqrt(3)/2
2cos^2x + cosx = 1
cosx(2cosx+1)=1
cosx = 1; 2cosx+1=1
Are the moves above correct? Explain.
No, you can only set each factored term equal to 0 if they multiply to be 0
2cos^2x + cosx = 1
2cos^2x + cosx - 1 = 0
(2cosx-1)(cosx+1)=0
2cosx-1=0; cosx+1=0
Convert (5pi)/6 to degrees
150 degrees
What is csc (5pi)/3 ?
-(2sqrt(3))/3
y=2/3cos(x/2-pi/4)
What is the period? What is the horizontal shift?
period = 4pi
Horizontal shift = pi/2 to the right
Rationalize 4/(2-sqrt(3)
8+4sqrt(3)
(sinx+1)/(sinx-1)=(sinx+1)/(sinx-1)*(sinx+1)/(sinx+1) = (sin^2x+1)/-cos^2
How was that math? Pretty good? Explain.
No.
(sinx+1)*(sinx+1) = sin^2x+2sinx+1
Determine the quadrant in which theta lie when csc<0 and tan>0
Quadrant III
What is arccos(sin((11pi)/6))
(2pi)/3
A ferris wheel is 30 meters tall, the center of axle is 20 meters off the ground and rotates every 20 minutes. What is the highest point that is reached by a passenger riding on the ferris wheel? What is the lowest point?
Highest point is 35 meters. Lowest point is 5 meters.
Rewrite the expression as the tangent of an single angle
(2tan(100))/(1-tan^2(100))
tan(200)
2sinxcosx=sinx
(2sinxcosx)/sinx = sinx/sinx
2cosx = 1
cosx = 1/2
What's wrong with the moves above?
2sinxcosx=sinx
2sinxcosx - sinx = 0
sinx(2cosx-1)=-
sinx= 0; 2cosx-1=0
By dividing sin on both side, we lost the solution sinx=0